2D Geometry Questions and Answers

4 4pts Determine the area of the shaded shapes in Figure 4 Show your work 1 unit Figure 4 Nam

Objective Calculate the degree measure of an arc using the arc addition postulate R S 94 O T U Segments RT and SU are diameters of circle O What is the degree measure of arc SRT Hint just give numerical answer do NOT write degrees or use the degree sign

14 6 points Objective Determine the measures of central angles chords and arcs using theorems about angle chord and arc congre P T 4 3 48 66 R S 66 In circle T ZPTQ ZRTS What is the measure of arc PQ 24 33

Objective Solve problems involving angles formed by two intersecting chorc K L 170 125 250 50 55 O A M J 80 In circle O what is the measure of ZMAJ

Objective Apply theorems about inscribed angles and angles formed by a tangent and T 34 V U S Line segment SU is a diameter of circle V What is the measure of arc ST 68 56 112

U 14 D 8 16 C 56 S T 28 Find the missing length The triangles are similar Type your answer

Objective Identify and describe terms related to circles Which circle has a radius that measure 10 units O O 10 10 G H 6 20 F 20

Objective Solve problems involving arc length with central angles measured in degrees Q R 123 P S In circle P diameter QS measures 20 centimeters What is the approximate length of arc QR 10 centimeters 22 centimeters 20 centimeters 43 centimeters

C IL M 72 O 16 8 33 L 24 B The triangles are similar What is the missing length 18

A Ferris wheel has a diameter of 42 feet It rotates 3 times per minute Approximately how far will a passenger travel during a 5 minute ride 3 956 feet 132 feet 659 feet 1 978 feet

Objective Determine segment lengths angle measures and arc measure A 15 C O 8 B 5 D E Angle D is a circumscribed angle of circle O What is the perimeter of kite OBDE 60 units 17 units 27 units 23 units

An airplane takes off and climbs must fly over a 120 foot tower w what is the minimum distance be leaves the ground and the base of Draw and label a diagram for thi

K 54 B 112 C 110 D 108 J L What is the measure of arc KL A 106

A planter shaped like a rectangular prism has a length of 4 meters a width of 4 meters and a height of 3 meters Attached to the side of the planter is a smaller planter with 1 the volume of the larger planter What is the combined volume of both planters 24 cubic meters 34 cubic meters 48 cubic meters 72 cubic meters

Identify the value of x and the length of each secant segment N MY 3 2 5 L O x 12 NL 8 NP 14 Ox 12 NL 14 NP 8 x 10 NL 8 NP 12 Ox 10 NL 12 NP 8 X

Find the value of the indicated angles 8b 1 6b 9

11 M 33 A L 24 B The triangles are similar What is the missing length

18 What is the domain AND range of the function given below Use proper interval notation or Write infinity as inf 8 2 BiUFE EXA

26 Multiply and simplify completely 3x 1 3x 1 6x 6x 1 B 6x 1 9x 1 D 9x Previous 6x 1

What are the solutions to the equation z 9 0 8 11

Write the polynomial as an expression of its simplest fac 7 14a 21a

4y k 7y 9 In the system of equations shown above j and k are Which of the following constants and j is k plus must be true A x is y minus B x is y plus 1 2 C x is y minus D x is y plus 9 2 1 2 3 2 3 2

A circular swimming pool has diameter k meters and depth 4 meters throughout Which of the following expressions give the amount of water it holds in Ocubic meters

116 M C N 2X 8 What is the measure of arc PN 232 degrees 62 degrees 116 degrees 54 degrees

The graph of a function f is illustrated in the figure below a Draw the graph of y f x b Draw the graph of y f x 2 5 A 4 0 2 5 Q Choose the correct graph of y f x below OA OC in q Fin Q OB OD 3 F5 Q O

7 Find the exponential function f x Cb whose graph is given The graph goes 8 points through the points 0 2 and 1 6

Given ZBAC LEDC and BC CE Prove AABC ADEC X B E Steps ZBAC LEDC BC CE LACBZDCE AABC ADEC D Reason Answer Answer Answer Answer

translate 5 units down and then rotate 90 degrees about the origin

Which statements about the right triangle are correct Select all that apply 3 points cosB 13 12 cotA 5 12 cscA 12 5 sinA 12 13 secB 13 12 tanA 5 12

Example 1 Let g x y a Find the domain of 9 Y b Sketch the level curves g x y c for c 1 0 2 Note Some authors prefer the term contour or conto instead of level curve

Find PR such that 0 PR 5 and m0 is a maximum Let a 2 b 7 and h 5 Round your answer to f PR C e R

42 0 in 128 0 in 42 0 in 16 0 in Triangular Right Prism with Isosceles Triangle Bases

2 5 points Match each of the functions with their respective level curves descriptions 0 x y 2 0 2x 3y 5z 7 z ln 2 y 215 92 4y 2 2y x x y A Unequally spaced concentric circles B Equally spaced concentric circles C Lines with a common intersection D Unequally spaced parallel lines E Equally spaced parallel lines

Topic Geometric proofs Complete each proof 29 Given NONP OQ PQ NO PQ NO DPQ numbers Prove ZNOP LOPQ Circled ter side F the tou nes are transversal Inlevior Perpendicular Perpendicular 90 Statements Par

3 4 1 point Look at the following right angle below What is the value for y Type your answer 5 y X 2 ft 1 point In ARST m R 73 and m S 56 Which statement about the sides of ARST must be true ST TR RS TR RS ST ST RS TR TR ST RS RS TR ST

A gate automatically opens when the water gets too high How high in cm above the hinge must the water be for the gate to just open if the location of the hinge is measured 80 from bottom Gate Water 11m Hinge

4 1 1 14 A 6x 63 4x 3 Line I is parallel to line m when the value of x is 38 12 30 3 1 point Max want to launch a projectile at a structure that is 335 feet away horizontally and 249 feet high What angle of elevation will he need to fire his projectile of at to hit the target on top of the structure 0 335 ft B 249 ft C

If AXYZ is reflected across the y axis to form AX Y Z what is the coordinate of Y 2 Y tyngYOU ancuor tung your onquer

19 Find the average Y coordinate of a point in the region below the parabola y 1 x and above the X axis

A horizontal 80 cm diameter hatch is located on the top of a submersibl designed for a river to escape If the submersible is 72 m below the surface of the ocean estimate the total force applied on the hatch Assume Ssaltwater 1 02 Answer Choose Choose

3 Clearly describe and or graph the set of all points r y at which the given function is continu Explain your reasoning 4 a f x y ccm ry 1 4 b g x y ln 2 y 5

0 Why are these triangles similar A B R SSS SAS AA Triangles are not similar X SAS C 1 point Why are these triangles similar A B SSS C Z X

Why are these triangles similar 4 LA 12 sss AA 3 O O Triangles are not similar SAS 1 1 point Why are these triangles similar

1 1 point Why are the triangles similar triangles are not similar SSS SAS AA 1 point Why are the triangles similar 44 2 SSS AA triangles are not similar 2

1 point What is the similarity ratio of these triangles 2 3 4 5 6 1 2 1 not similar 4 1 point Why are these triangles similar AV SSS Triangles are not similar 2

1 point Why are these triangles similar 9 6 Osss 6 SAS AA 9 7 Triangles are not similar 1 point Why are these triangles similar SSS 3 12 2 14 3 Triangles are not similar

Solve the right triangle shown in the figure for all unknown sides and angles Round your answers to two decimal places A 5 8 a 36 5 B 11 0 b B a C E D A Q

A DVD rotates through and angle of 201 radians in 1 second That means it times around in 1 rotates second If it rotates that number of times in 1 second how many times does it rotate in 1 minute revolutions per minute

Find the Galois group of the following polynomials a x x 2x 2x 1 over Q b x 10 over Q 2

What is the measure in radians of the angle A 45 Select one O a 2 3 O b 2 O C 7 12 O d 4